2019-01-18

ION HANCU

ION HANCU

2019-01-29

MARIA MAFFEI

MARIA MAFFEI

2019-02-13

BORIS BOURDONCLE

BORIS BOURDONCLE

2019-02-15

JORDI MORALES DALMAU

JORDI MORALES DALMAU

2019-02-22

FRANCESCO RICCI

FRANCESCO RICCI

2019-03-06

CLARA GREGORI

CLARA GREGORI

2019-03-26

ALEXIA SALAVRAKOS

ALEXIA SALAVRAKOS

2019-04-12

SENAIDA HERNANDEZ SANTANA

SENAIDA HERNANDEZ SANTANA

2019-04-15

DAVID RAVENTÓS RIBERA

DAVID RAVENTÓS RIBERA

2019-04-16

PETER SCHMIDT

PETER SCHMIDT

2019-04-29

CALLUM O’DONNELL

CALLUM O’DONNELL

2019-05-02

LUCIANA VIDAS

LUCIANA VIDAS

2019-05-03

HANYU YE

HANYU YE

2019-05-10

TANJA DRAGOJEVIC

TANJA DRAGOJEVIC

2019-05-17

FLAVIO BACCARI

FLAVIO BACCARI

2019-06-04

MARTINA GIOVANNELLA

MARTINA GIOVANNELLA

### Quantifying Randomness from Bell Nonlocality

BORIS BOURDONCLE

**February 13th, 2019**

**BORIS BOURDONCLE**

**Quantum Information Theory**

ICFO-The Institute of Photonic Sciences

ICFO-The Institute of Photonic Sciences

The twentieth century was marked by two scientific revolutions. On the one hand, quantum mechanics questioned our understanding of nature and physics. On the other hand, came the realisation that information could be treated as a mathematical quantity. They together brought forward the age of information.

A conceptual leap took place in the 1980’s, that consisted in treating information in a quantum way as well. The idea that the intuitive notion of information could be governed by the counter-intuitive laws of quantum mechanics proved extremely fruitful, both from fundamental and applied points of view.

The notion of randomness plays a central role in that respect. Indeed, the laws of quantum physics are probabilistic: that contrasts with thousands of years of physical theories that aimed to derive deterministic laws of nature. This, in turn, provides us with sources of random numbers, a crucial resource for information protocols.

The fact that quantum theory only describes probabilistic behaviours was for some time regarded as a form of incompleteness. But nonlocality, in the sense of Bell, showed that this was not the case: the laws of quantum physics are inherently random, i.e., the randomness they imply cannot be traced back to a lack of knowledge.

This observation has practical consequences: the outputs of a nonlocal physical process are necessarily unpredictable. Moreover, the random character of these outputs does not depend on the physical system, but only of its nonlocal character. For that reason, nonlocality-based randomness is certified in a device-independent manner.

In this thesis, we quantify nonlocality-based randomness in various frameworks. In the first scenario, we quantify randomness without relying on the quantum formalism. We consider a nonlocal process and assume that it has a specific causal structure that is only due to how it evolves with time. We provide trade-offs between nonlocality and randomness for the various causal structures that we consider.

Nonlocality-based randomness is usually defined in a theoretical framework. In the second scenario, we take a practical approach and ask how much randomness can be certified in a practical situation, where only partial information can be gained from an experiment. We describe a method to optimise how much randomness can be certified in such a situation.

Trade-offs between nonlocality and randomness are usually studied in the bipartite case, as two agents is the minimal requirement to define nonlocality. In the third scenario, we quantify how much randomness can be certified for a tripartite process.

Though nonlocality-based randomness is device-independent, the process from which randomness is certified is actually realised with a physical state. In the fourth scenario, we ask what physical requirements should be imposed on the physical state for maximal randomness to be certified, and more specifically, how entangled the underlying state should be. We show that maximal randomness can be certified from any level of entanglement.

**Wednesday, February 13, 11:00. ICFO Auditorium**

Thesis Advisor: Prof Dr Antonio Acin

Thesis Advisor: Prof Dr Antonio Acin